Add mobius function (#3241)

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Akshay Dubey 2022-09-03 12:04:06 +05:30 committed by GitHub
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package com.thealgorithms.maths;
/*
* Java program for mobius function
* For any positive integer n, define μ(n) as the sum of the primitive nth roots of unity.
* It has values in {1, 0, 1} depending on the factorization of n into prime factors:
* μ(n) = +1 if n is a square-free positive integer with an even number of prime factors.
* μ(n) = 1 if n is a square-free positive integer with an odd number of prime factors.
* μ(n) = 0 if n has a squared prime factor.
* Wikipedia: https://en.wikipedia.org/wiki/M%C3%B6bius_function
*
* Author: Akshay Dubey (https://github.com/itsAkshayDubey)
*
* */
public class MobiusFunction {
/**
* This method returns μ(n) of given number n
*
* @param number Integer value which μ(n) is to be calculated
* @return 1 when number is less than or equals 1
* or number has even number of prime factors
* 0 when number has repeated prime factor
* -1 when number has odd number of prime factors
*/
static int mobius(int number) {
if(number <= 0) {
//throw exception when number is less than or is zero
throw new IllegalArgumentException("Number must be greater than zero.");
}
if(number == 1) {
//return 1 if number passed is less or is 1
return 1;
}
int primeFactorCount=0;
for(int i = 1; i <= number; i++) {
//find prime factors of number
if(number % i == 0 && PrimeCheck.isPrime(i)) {
//check if number is divisible by square of prime factor
if(number % (i*i) == 0) {
//if number is divisible by square of prime factor
return 0;
}
/*increment primeFactorCount by 1
if number is not divisible by square of found prime factor*/
primeFactorCount++;
}
}
return (primeFactorCount % 2 == 0) ? 1 : -1;
}
}

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package com.thealgorithms.maths;
import static org.junit.jupiter.api.Assertions.*;
import org.junit.jupiter.api.Test;
class MobiusFunctionTest {
@Test
void testMobiusForZero() {
//given
int number = 0;
String expectedMessage = "Number must be greater than zero.";
//when
Exception exception = assertThrows(IllegalArgumentException.class, () -> {
MobiusFunction.mobius(number);
});
String actualMessage = exception.getMessage();
//then
assertEquals(expectedMessage, actualMessage);
}
@Test
void testMobiusForNegativeNumber() {
//given
int number = -1;
String expectedMessage = "Number must be greater than zero.";
//when
Exception exception = assertThrows(IllegalArgumentException.class, () -> {
MobiusFunction.mobius(number);
});
String actualMessage = exception.getMessage();
//then
assertEquals(expectedMessage, actualMessage);
}
@Test
void testMobiusFunction(){
int[] expectedResultArray = {
1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -1, 0,
0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0,
0, 1, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1,
0, 0, 1, -1, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0, -1, 0, 1, 0, 1, 1, 1, 0, -1, 0, 0, 0
};
for(int i = 1; i <= 100; i++) {
//given
int expectedValue = expectedResultArray[i-1];
//when
int actualValue = MobiusFunction.mobius(i);
//then
assertEquals(expectedValue,actualValue);
}
}
}